Question

Which expression can be used to find the length of AT?

12.5/cos 66
12.5(cos66)
12.5/sin66
12.5(sin66)

Answer 1

`\large\boxed{\large\boxed{\overline{AT}=12.5(cos66\º)}}`

Step-by-step explanation:

In a right triangle the angle between the hypotenuse and the adjacent leg to the angle are related by the trigonometric ratio cosine.

Cosine is the ratio of the adjacent leg to the hypotenuse:

In the right triangle ART, AT is the hypotenuse, AR is the ajacent leg to the angle 66º, and RT is the opposite leg to the angle 66º.

Then, the length of AT and 12.5 is related by the cosine ratio:

`cos(66\º)=\frac{\overline{AT}}{12.5}`

Multiplying both sides of the equation by 12.5in:

`\overline{AT}=12.5(cos66\º)` ← answer